LMFDB - Embedded newform 2100.2.d.d.1301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1301,2100)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2100.1301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1301.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2100.1301
Dual form			2100.2.d.d.1301.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205i q^{3} +(0.500000 + 2.59808i) q^{7} -3.00000 q^{9} -1.73205i q^{13} +5.19615i q^{19} +(4.50000 - 0.866025i) q^{21} +5.19615i q^{27} +1.73205i q^{31} +10.0000 q^{37} -3.00000 q^{39} +13.0000 q^{43} +(-6.50000 + 2.59808i) q^{49} +9.00000 q^{57} +15.5885i q^{61} +(-1.50000 - 7.79423i) q^{63} +11.0000 q^{67} +13.8564i q^{73} -4.00000 q^{79} +9.00000 q^{81} +(4.50000 - 0.866025i) q^{91} +3.00000 q^{93} -5.19615i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{7} - 6 q^{9} + 9 q^{21} + 20 q^{37} - 6 q^{39} + 26 q^{43} - 13 q^{49} + 18 q^{57} - 3 q^{63} + 22 q^{67} - 8 q^{79} + 18 q^{81} + 9 q^{91} + 6 q^{93}+O(q^{100}) $ 2 * q + q^7 - 6 * q^9 + 9 * q^21 + 20 * q^37 - 6 * q^39 + 26 * q^43 - 13 * q^49 + 18 * q^57 - 3 * q^63 + 22 * q^67 - 8 * q^79 + 18 * q^81 + 9 * q^91 + 6 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$		0			0
$9$	−3.00000			−1.00000
$10$		0			0
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$		0			0
$13$		−	1.73205i		−	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$		−	1.73205i		−	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$			5.19615i			1.19208i	0.802955	+	0.596040i	$0.203260\pi$
$19$			5.19615i			1.19208i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	4.50000	−	0.866025i	0.981981	−	0.188982i
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$			1.73205i			0.311086i	0.987829	+	0.155543i	$0.0497126\pi$
$31$			1.73205i			0.311086i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	10.0000			1.64399			0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000			1.64399			0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$	−3.00000			−0.480384
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	13.0000			1.98248			0.991241	−	0.132068i	$-0.0421616\pi$
$43$	13.0000			1.98248			0.991241	+	0.132068i	$0.0421616\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	9.00000			1.19208
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$			15.5885i			1.99590i	0.0640184	+	0.997949i	$0.479608\pi$
$61$			15.5885i			1.99590i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$		0			0
$63$	−1.50000	−	7.79423i	−0.188982	−	0.981981i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	11.0000			1.34386			0.671932	−	0.740613i	$-0.265465\pi$
$67$	11.0000			1.34386			0.671932	+	0.740613i	$0.265465\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$			13.8564i			1.62177i	0.585206	+	0.810885i	$0.301014\pi$
$73$			13.8564i			1.62177i	−0.585206	+	0.810885i	$0.698986\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$	4.50000	−	0.866025i	0.471728	−	0.0907841i
$92$		0			0
$93$	3.00000			0.311086
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	5.19615i		−	0.527589i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$		−	5.19615i		−	0.527589i	0.964579	−	0.263795i	$-0.0849741\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$			3.46410i			0.341328i	0.985329	+	0.170664i	$0.0545913\pi$
$103$			3.46410i			0.341328i	−0.985329	+	0.170664i	$0.945409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	−17.0000			−1.62830			−0.814152	−	0.580651i	$-0.802798\pi$
$109$	−17.0000			−1.62830			−0.814152	+	0.580651i	$0.802798\pi$
$110$		0			0
$111$		−	17.3205i		−	1.64399i
$112$		0			0
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$			5.19615i			0.480384i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	11.0000			1.00000
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$		0			0
$129$		−	22.5167i		−	1.98248i
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−13.5000	+	2.59808i	−1.17060	+	0.225282i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$		0			0
$139$		−	17.3205i		−	1.46911i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$		−	17.3205i		−	1.46911i	0.678551	−	0.734553i	$-0.262608\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	4.50000	+	11.2583i	0.371154	+	0.928571i
$148$		0			0
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$		0			0
$151$	19.0000			1.54620			0.773099	−	0.634285i	$-0.218706\pi$
$151$	19.0000			1.54620			0.773099	+	0.634285i	$0.218706\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	22.5167i		−	1.79703i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$		−	22.5167i		−	1.79703i	0.438948	−	0.898513i	$-0.355351\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	17.0000			1.33154			0.665771	−	0.746156i	$-0.268103\pi$
$163$	17.0000			1.33154			0.665771	+	0.746156i	$0.268103\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	10.0000			0.769231
$170$		0			0
$171$		−	15.5885i		−	1.19208i
$172$		0			0
$173$		0			0			−	1.00000i	$-0.5\pi$
$173$		0			0				1.00000i	$0.5\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$		0			0
$181$			19.0526i			1.41617i	0.706129	+	0.708083i	$0.250440\pi$
$181$			19.0526i			1.41617i	−0.706129	+	0.708083i	$0.749560\pi$
$182$		0			0
$183$	27.0000			1.99590
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−13.5000	+	2.59808i	−0.981981	+	0.188982i
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$		0			0
$193$	−23.0000			−1.65558			−0.827788	−	0.561041i	$-0.810401\pi$
$193$	−23.0000			−1.65558			−0.827788	+	0.561041i	$0.810401\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$		−	22.5167i		−	1.59616i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$		−	22.5167i		−	1.59616i	0.602549	−	0.798082i	$-0.294152\pi$
$200$		0			0
$201$		−	19.0526i		−	1.34386i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−29.0000			−1.99644			−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−29.0000			−1.99644			−0.998221	+	0.0596196i	$0.981011\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−4.50000	+	0.866025i	−0.305480	+	0.0587896i
$218$		0			0
$219$	24.0000			1.62177
$220$		0			0
$221$		0			0
$222$		0			0
$223$			19.0526i			1.27585i	0.770097	+	0.637927i	$0.220208\pi$
$223$			19.0526i			1.27585i	−0.770097	+	0.637927i	$0.779792\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0			−	1.00000i	$-0.5\pi$
$227$		0			0				1.00000i	$0.5\pi$
$228$		0			0
$229$			29.4449i			1.94577i	0.231287	+	0.972886i	$0.425707\pi$
$229$			29.4449i			1.94577i	−0.231287	+	0.972886i	$0.574293\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			6.92820i			0.450035i
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$			1.73205i			0.111571i	0.998443	+	0.0557856i	$0.0177663\pi$
$241$			1.73205i			0.111571i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$		0			0
$243$		−	15.5885i		−	1.00000i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	9.00000			0.572656
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$		0			0			−	1.00000i	$-0.5\pi$
$257$		0			0				1.00000i	$0.5\pi$
$258$		0			0
$259$	5.00000	+	25.9808i	0.310685	+	1.61437i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$			17.3205i			1.05215i	0.850439	+	0.526073i	$0.176336\pi$
$271$			17.3205i			1.05215i	−0.850439	+	0.526073i	$0.823664\pi$
$272$		0			0
$273$	−1.50000	−	7.79423i	−0.0907841	−	0.471728i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−31.0000			−1.86261			−0.931305	−	0.364241i	$-0.881328\pi$
$277$	−31.0000			−1.86261			−0.931305	+	0.364241i	$0.881328\pi$
$278$		0			0
$279$		−	5.19615i		−	0.311086i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$		0			0
$283$			32.9090i			1.95623i	0.208053	+	0.978117i	$0.433287\pi$
$283$			32.9090i			1.95623i	−0.208053	+	0.978117i	$0.566713\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−17.0000			−1.00000
$290$		0			0
$291$	−9.00000			−0.527589
$292$		0			0
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	6.50000	+	33.7750i	0.374654	+	1.94676i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	29.4449i		−	1.68051i	−0.542194	−	0.840254i	$-0.682406\pi$
$307$		−	29.4449i		−	1.68051i	0.542194	−	0.840254i	$-0.317594\pi$
$308$		0			0
$309$	6.00000			0.341328
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$		−	32.9090i		−	1.86012i	−0.367402	−	0.930062i	$-0.619753\pi$
$313$		−	32.9090i		−	1.86012i	0.367402	−	0.930062i	$-0.380247\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$			29.4449i			1.62830i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−32.0000			−1.75888			−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−32.0000			−1.75888			−0.879440	+	0.476011i	$0.842082\pi$
$332$		0			0
$333$	−30.0000			−1.64399
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−29.0000			−1.57973			−0.789865	−	0.613280i	$-0.789850\pi$
$337$	−29.0000			−1.57973			−0.789865	+	0.613280i	$0.789850\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		1.00000			$0$
$347$		0			0		−1.00000			$\pi$
$348$		0			0
$349$			34.6410i			1.85429i	0.374701	+	0.927146i	$0.377745\pi$
$349$			34.6410i			1.85429i	−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	9.00000			0.480384
$352$		0			0
$353$		0			0			−	1.00000i	$-0.5\pi$
$353$		0			0				1.00000i	$0.5\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$	−8.00000			−0.421053
$362$		0			0
$363$		−	19.0526i		−	1.00000i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		−	22.5167i		−	1.17536i	−0.809093	−	0.587680i	$-0.800041\pi$
$367$		−	22.5167i		−	1.17536i	0.809093	−	0.587680i	$-0.199959\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−13.0000			−0.673114			−0.336557	−	0.941663i	$-0.609263\pi$
$373$	−13.0000			−0.673114			−0.336557	+	0.941663i	$0.609263\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	37.0000			1.90056			0.950281	−	0.311393i	$-0.100796\pi$
$379$	37.0000			1.90056			0.950281	+	0.311393i	$0.100796\pi$
$380$		0			0
$381$		−	34.6410i		−	1.77471i
$382$		0			0
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−39.0000			−1.98248
$388$		0			0
$389$		0			0		1.00000			$0$
$389$		0			0		−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$			39.8372i			1.99937i	0.0250943	+	0.999685i	$0.492011\pi$
$397$			39.8372i			1.99937i	−0.0250943	+	0.999685i	$0.507989\pi$
$398$		0			0
$399$	4.50000	+	23.3827i	0.225282	+	1.17060i
$400$		0			0
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$	3.00000			0.149441
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$		−	39.8372i		−	1.96982i	−0.173064	−	0.984911i	$-0.555367\pi$
$409$		−	39.8372i		−	1.96982i	0.173064	−	0.984911i	$-0.444633\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−30.0000			−1.46911
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−40.5000	+	7.79423i	−1.95993	+	0.377189i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$		0			0
$433$			19.0526i			0.915608i	0.889053	+	0.457804i	$0.151364\pi$
$433$			19.0526i			0.915608i	−0.889053	+	0.457804i	$0.848636\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$			39.8372i			1.90132i	0.310228	+	0.950662i	$0.399595\pi$
$439$			39.8372i			1.90132i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$	19.5000	−	7.79423i	0.928571	−	0.371154i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		−	32.9090i		−	1.54620i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	10.0000			0.467780			0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000			0.467780			0.233890	+	0.972263i	$0.424854\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$	20.0000			0.929479			0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000			0.929479			0.464739	+	0.885448i	$0.346148\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$		0			0
$469$	5.50000	+	28.5788i	0.253966	+	1.31965i
$470$		0			0
$471$	−39.0000			−1.79703
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$		−	17.3205i		−	0.789747i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$	19.0000			0.860972			0.430486	−	0.902597i	$-0.358342\pi$
$487$	19.0000			0.860972			0.430486	+	0.902597i	$0.358342\pi$
$488$		0			0
$489$		−	29.4449i		−	1.33154i
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	43.0000			1.92494			0.962472	−	0.271380i	$-0.0874801\pi$
$499$	43.0000			1.92494			0.962472	+	0.271380i	$0.0874801\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	17.3205i		−	0.769231i
$508$		0			0
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$		0			0
$511$	−36.0000	+	6.92820i	−1.59255	+	0.306486i
$512$		0			0
$513$	−27.0000			−1.19208
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$		0			0
$523$			15.5885i			0.681636i	0.940129	+	0.340818i	$0.110704\pi$
$523$			15.5885i			0.681636i	−0.940129	+	0.340818i	$0.889296\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	23.0000			1.00000
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	29.0000			1.24681			0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000			1.24681			0.623404	+	0.781900i	$0.285749\pi$
$542$		0			0
$543$	33.0000			1.41617
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−40.0000			−1.71028			−0.855138	−	0.518400i	$-0.826528\pi$
$547$	−40.0000			−1.71028			−0.855138	+	0.518400i	$0.826528\pi$
$548$		0			0
$549$		−	46.7654i		−	1.99590i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−2.00000	−	10.3923i	−0.0850487	−	0.441926i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		1.00000			$0$
$557$		0			0		−1.00000			$\pi$
$558$		0			0
$559$		−	22.5167i		−	0.952353i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0			−	1.00000i	$-0.5\pi$
$563$		0			0				1.00000i	$0.5\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	4.50000	+	23.3827i	0.188982	+	0.981981i
$568$		0			0
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$	−31.0000			−1.29731			−0.648655	−	0.761083i	$-0.724668\pi$
$571$	−31.0000			−1.29731			−0.648655	+	0.761083i	$0.724668\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	46.7654i		−	1.94687i	−0.228968	−	0.973434i	$-0.573535\pi$
$577$		−	46.7654i		−	1.94687i	0.228968	−	0.973434i	$-0.426465\pi$
$578$		0			0
$579$			39.8372i			1.65558i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0			−	1.00000i	$-0.5\pi$
$587$		0			0				1.00000i	$0.5\pi$
$588$		0			0
$589$	−9.00000			−0.370839
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−39.0000			−1.59616
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$		−	1.73205i		−	0.0706518i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$		−	1.73205i		−	0.0706518i	0.999376	−	0.0353259i	$-0.0112469\pi$
$602$		0			0
$603$	−33.0000			−1.34386
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	45.0333i		−	1.82785i	−0.405887	−	0.913923i	$-0.633038\pi$
$607$		−	45.0333i		−	1.82785i	0.405887	−	0.913923i	$-0.366962\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−10.0000			−0.403896			−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000			−0.403896			−0.201948	+	0.979396i	$0.564727\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$		−	46.7654i		−	1.87966i	−0.341644	−	0.939829i	$-0.610984\pi$
$619$		−	46.7654i		−	1.87966i	0.341644	−	0.939829i	$-0.389016\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.00000			−0.0398094			−0.0199047	−	0.999802i	$-0.506336\pi$
$631$	−1.00000			−0.0398094			−0.0199047	+	0.999802i	$0.506336\pi$
$632$		0			0
$633$			50.2295i			1.99644i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	4.50000	+	11.2583i	0.178296	+	0.446071i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$		0			0
$643$			31.1769i			1.22950i	0.788723	+	0.614749i	$0.210743\pi$
$643$			31.1769i			1.22950i	−0.788723	+	0.614749i	$0.789257\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	1.50000	+	7.79423i	0.0587896	+	0.305480i
$652$		0			0
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	41.5692i		−	1.62177i
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$		−	34.6410i		−	1.34738i	−0.739014	−	0.673690i	$-0.764708\pi$
$661$		−	34.6410i		−	1.34738i	0.739014	−	0.673690i	$-0.235292\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	33.0000			1.27585
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−50.0000			−1.92736			−0.963679	−	0.267063i	$-0.913947\pi$
$673$	−50.0000			−1.92736			−0.963679	+	0.267063i	$0.913947\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$		0			0
$679$	13.5000	−	2.59808i	0.518082	−	0.0997050i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	51.0000			1.94577
$688$		0			0
$689$		0			0
$690$		0			0
$691$			51.9615i			1.97671i	0.152167	+	0.988355i	$0.451375\pi$
$691$			51.9615i			1.97671i	−0.152167	+	0.988355i	$0.548625\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$			51.9615i			1.95977i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−53.0000			−1.99046			−0.995228	−	0.0975728i	$-0.968892\pi$
$709$	−53.0000			−1.99046			−0.995228	+	0.0975728i	$0.968892\pi$
$710$		0			0
$711$	12.0000			0.450035
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	−9.00000	+	1.73205i	−0.335178	+	0.0645049i
$722$		0			0
$723$	3.00000			0.111571
$724$		0			0
$725$		0			0
$726$		0			0
$727$			22.5167i			0.835097i	0.908655	+	0.417548i	$0.137111\pi$
$727$			22.5167i			0.835097i	−0.908655	+	0.417548i	$0.862889\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$		0			0
$732$		0			0
$733$		−	20.7846i		−	0.767697i	−0.923396	−	0.383849i	$-0.874598\pi$
$733$		−	20.7846i		−	0.767697i	0.923396	−	0.383849i	$-0.125402\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−16.0000			−0.588570			−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000			−0.588570			−0.294285	+	0.955718i	$0.595081\pi$
$740$		0			0
$741$		−	15.5885i		−	0.572656i
$742$		0			0
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	52.0000			1.89751			0.948753	−	0.316017i	$-0.102346\pi$
$751$	52.0000			1.89751			0.948753	+	0.316017i	$0.102346\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−29.0000			−1.05402			−0.527011	−	0.849858i	$-0.676688\pi$
$757$	−29.0000			−1.05402			−0.527011	+	0.849858i	$0.676688\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0			−	1.00000i	$-0.5\pi$
$761$		0			0				1.00000i	$0.5\pi$
$762$		0			0
$763$	−8.50000	−	44.1673i	−0.307721	−	1.59896i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		−	29.4449i		−	1.06181i	−0.847432	−	0.530904i	$-0.821852\pi$
$769$		−	29.4449i		−	1.06181i	0.847432	−	0.530904i	$-0.178148\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0			−	1.00000i	$-0.5\pi$
$773$		0			0				1.00000i	$0.5\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	45.0000	−	8.66025i	1.61437	−	0.310685i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$		−	46.7654i		−	1.66701i	−0.552515	−	0.833503i	$-0.686332\pi$
$787$		−	46.7654i		−	1.66701i	0.552515	−	0.833503i	$-0.313668\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	27.0000			0.958798
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$		0			0
$811$		−	53.6936i		−	1.88544i	−0.333590	−	0.942718i	$-0.608260\pi$
$811$		−	53.6936i		−	1.88544i	0.333590	−	0.942718i	$-0.391740\pi$
$812$		0			0
$813$	30.0000			1.05215
$814$		0			0
$815$		0			0
$816$		0			0
$817$			67.5500i			2.36327i
$818$		0			0
$819$	−13.5000	+	2.59808i	−0.471728	+	0.0907841i
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$		0			0
$823$	47.0000			1.63832			0.819159	−	0.573567i	$-0.194441\pi$
$823$	47.0000			1.63832			0.819159	+	0.573567i	$0.194441\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$		0			0
$829$		−	34.6410i		−	1.20313i	−0.798823	−	0.601566i	$-0.794544\pi$
$829$		−	34.6410i		−	1.20313i	0.798823	−	0.601566i	$-0.205456\pi$
$830$		0			0
$831$			53.6936i			1.86261i
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−9.00000			−0.311086
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$		0			0
$847$	5.50000	+	28.5788i	0.188982	+	0.981981i
$848$		0			0
$849$	57.0000			1.95623
$850$		0			0
$851$		0			0
$852$		0			0
$853$		−	53.6936i		−	1.83843i	−0.393753	−	0.919216i	$-0.628823\pi$
$853$		−	53.6936i		−	1.83843i	0.393753	−	0.919216i	$-0.371177\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$			17.3205i			0.590968i	0.955348	+	0.295484i	$0.0954809\pi$
$859$			17.3205i			0.590968i	−0.955348	+	0.295484i	$0.904519\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			29.4449i			1.00000i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		−	19.0526i		−	0.645571i
$872$		0			0
$873$			15.5885i			0.527589i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	59.0000			1.99229			0.996144	−	0.0877308i	$-0.0279615\pi$
$877$	59.0000			1.99229			0.996144	+	0.0877308i	$0.0279615\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	−47.0000			−1.58168			−0.790838	−	0.612026i	$-0.790355\pi$
$883$	−47.0000			−1.58168			−0.790838	+	0.612026i	$0.790355\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0			−	1.00000i	$-0.5\pi$
$887$		0			0				1.00000i	$0.5\pi$
$888$		0			0
$889$	10.0000	+	51.9615i	0.335389	+	1.74273i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$	58.5000	−	11.2583i	1.94676	−	0.374654i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	40.0000			1.32818			0.664089	−	0.747653i	$-0.268820\pi$
$907$	40.0000			1.32818			0.664089	+	0.747653i	$0.268820\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−53.0000			−1.74831			−0.874154	−	0.485648i	$-0.838584\pi$
$919$	−53.0000			−1.74831			−0.874154	+	0.485648i	$0.838584\pi$
$920$		0			0
$921$	−51.0000			−1.68051
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		−	10.3923i		−	0.341328i
$928$		0			0
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$		0			0
$931$	−13.5000	−	33.7750i	−0.442445	−	1.10693i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	5.19615i		−	0.169751i	−0.996392	−	0.0848755i	$-0.972951\pi$
$937$		−	5.19615i		−	0.169751i	0.996392	−	0.0848755i	$-0.0270492\pi$
$938$		0			0
$939$	−57.0000			−1.86012
$940$		0			0
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$		0			0
$949$	24.0000			0.779073
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	28.0000			0.903226
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	20.0000			0.643157			0.321578	−	0.946883i	$-0.395787\pi$
$967$	20.0000			0.643157			0.321578	+	0.946883i	$0.395787\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		0			0
$973$	45.0000	−	8.66025i	1.44263	−	0.277635i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		1.00000			$0$
$977$		0			0		−1.00000			$\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	51.0000			1.62830
$982$		0			0
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	61.0000			1.93773			0.968864	−	0.247592i	$-0.0796392\pi$
$991$	61.0000			1.93773			0.968864	+	0.247592i	$0.0796392\pi$
$992$		0			0
$993$			55.4256i			1.75888i
$994$		0			0
$995$		0			0
$996$		0			0
$997$			62.3538i			1.97477i	0.158352	+	0.987383i	$0.449382\pi$
$997$			62.3538i			1.97477i	−0.158352	+	0.987383i	$0.550618\pi$
$998$		0			0
$999$			51.9615i			1.64399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.d.d.1301.1	yes	2
3.2	odd	2	CM	2100.2.d.d.1301.1	yes	2
5.2	odd	4		2100.2.f.f.1049.2		4
5.3	odd	4		2100.2.f.f.1049.3		4
5.4	even	2		2100.2.d.c.1301.2	yes	2
7.6	odd	2	inner	2100.2.d.d.1301.2	yes	2
15.2	even	4		2100.2.f.f.1049.2		4
15.8	even	4		2100.2.f.f.1049.3		4
15.14	odd	2		2100.2.d.c.1301.2	yes	2
21.20	even	2	inner	2100.2.d.d.1301.2	yes	2
35.13	even	4		2100.2.f.f.1049.1		4
35.27	even	4		2100.2.f.f.1049.4		4
35.34	odd	2		2100.2.d.c.1301.1	✓	2
105.62	odd	4		2100.2.f.f.1049.4		4
105.83	odd	4		2100.2.f.f.1049.1		4
105.104	even	2		2100.2.d.c.1301.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.d.c.1301.1	✓	2	35.34	odd	2
2100.2.d.c.1301.1	✓	2	105.104	even	2
2100.2.d.c.1301.2	yes	2	5.4	even	2
2100.2.d.c.1301.2	yes	2	15.14	odd	2
2100.2.d.d.1301.1	yes	2	1.1	even	1	trivial
2100.2.d.d.1301.1	yes	2	3.2	odd	2	CM
2100.2.d.d.1301.2	yes	2	7.6	odd	2	inner
2100.2.d.d.1301.2	yes	2	21.20	even	2	inner
2100.2.f.f.1049.1		4	35.13	even	4
2100.2.f.f.1049.1		4	105.83	odd	4
2100.2.f.f.1049.2		4	5.2	odd	4
2100.2.f.f.1049.2		4	15.2	even	4
2100.2.f.f.1049.3		4	5.3	odd	4
2100.2.f.f.1049.3		4	15.8	even	4
2100.2.f.f.1049.4		4	35.27	even	4
2100.2.f.f.1049.4		4	105.62	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{3} +(0.500000 + 2.59808i) q^{7} -3.00000 q^{9} -1.73205i q^{13} +5.19615i q^{19} +(4.50000 - 0.866025i) q^{21} +5.19615i q^{27} +1.73205i q^{31} +10.0000 q^{37} -3.00000 q^{39} +13.0000 q^{43} +(-6.50000 + 2.59808i) q^{49} +9.00000 q^{57} +15.5885i q^{61} +(-1.50000 - 7.79423i) q^{63} +11.0000 q^{67} +13.8564i q^{73} -4.00000 q^{79} +9.00000 q^{81} +(4.50000 - 0.866025i) q^{91} +3.00000 q^{93} -5.19615i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{7} - 6 q^{9} + 9 q^{21} + 20 q^{37} - 6 q^{39} + 26 q^{43} - 13 q^{49} + 18 q^{57} - 3 q^{63} + 22 q^{67} - 8 q^{79} + 18 q^{81} + 9 q^{91} + 6 q^{93}+O(q^{100}) \) 2 * q + q^7 - 6 * q^9 + 9 * q^21 + 20 * q^37 - 6 * q^39 + 26 * q^43 - 13 * q^49 + 18 * q^57 - 3 * q^63 + 22 * q^67 - 8 * q^79 + 18 * q^81 + 9 * q^91 + 6 * q^93

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